An original sample of K-40 has a mass of 25.00 grams. After 3.9 m 109 years, 3.125 grams of the original sample remains unchanged. What is the half-life of K-40?

An original sample of K-40 has a mass of 25.00 grams. After 3.9 m 109 years, 3.125 grams of the original sample remains unchanged. What is the half-life of K-40?

First step is to determine the remaining decimal amount.

3.125 grams / 25.00 grams = 0.125

Second step is to determine the number of half lives.

(1/2) ^n = 0.125

N log (1/2) = log 0.125

N = 3 years